Pattern Formation and Localized Structures in Degenerate Optical Parametric Mixing

We report the pattern formation of degenerate optical parametric mixing---a system with the real-valued order parameter. The phenomena have similarities with and extend those of chemical and hydrodynamic systems described by real order parameter equations, and are different from laser-type pattern formation, where the order parameter is complex. The structure formation is based on a phase bistability. Structures are dominated by fronts separating domains of opposite phase. The domains expand or shrink depending on resonator detuning. Small circular domains, however, are stable and constitute the localized structures of the system. The phenomena are demonstrated experimentally using degenerate four-wave mixing as a prototype process in a resonator of a large Fresnel number.